writing null hypothesis examples

9.1 Null and Alternative Hypotheses

The actual test begins by considering two hypotheses . They are called the null hypothesis and the alternative hypothesis . These hypotheses contain opposing viewpoints.

H 0 , the — null hypothesis: a statement of no difference between sample means or proportions or no difference between a sample mean or proportion and a population mean or proportion. In other words, the difference equals 0.

H a —, the alternative hypothesis: a claim about the population that is contradictory to H 0 and what we conclude when we reject H 0 .

Since the null and alternative hypotheses are contradictory, you must examine evidence to decide if you have enough evidence to reject the null hypothesis or not. The evidence is in the form of sample data.

After you have determined which hypothesis the sample supports, you make a decision. There are two options for a decision. They are reject H 0 if the sample information favors the alternative hypothesis or do not reject H 0 or decline to reject H 0 if the sample information is insufficient to reject the null hypothesis.

Mathematical Symbols Used in H 0 and H a :

H 0 always has a symbol with an equal in it. H a never has a symbol with an equal in it. The choice of symbol depends on the wording of the hypothesis test. However, be aware that many researchers use = in the null hypothesis, even with > or < as the symbol in the alternative hypothesis. This practice is acceptable because we only make the decision to reject or not reject the null hypothesis.

Example 9.1

H 0 : No more than 30 percent of the registered voters in Santa Clara County voted in the primary election. p ≤ 30 H a : More than 30 percent of the registered voters in Santa Clara County voted in the primary election. p > 30

A medical trial is conducted to test whether or not a new medicine reduces cholesterol by 25 percent. State the null and alternative hypotheses.

Example 9.2

We want to test whether the mean GPA of students in American colleges is different from 2.0 (out of 4.0). The null and alternative hypotheses are the following: H 0 : μ = 2.0 H a : μ ≠ 2.0

We want to test whether the mean height of eighth graders is 66 inches. State the null and alternative hypotheses. Fill in the correct symbol (=, ≠, ≥, <, ≤, >) for the null and alternative hypotheses.

• H 0 : μ __ 66
• H a : μ __ 66

Example 9.3

We want to test if college students take fewer than five years to graduate from college, on the average. The null and alternative hypotheses are the following: H 0 : μ ≥ 5 H a : μ < 5

We want to test if it takes fewer than 45 minutes to teach a lesson plan. State the null and alternative hypotheses. Fill in the correct symbol ( =, ≠, ≥, <, ≤, >) for the null and alternative hypotheses.

• H 0 : μ __ 45
• H a : μ __ 45

Example 9.4

An article on school standards stated that about half of all students in France, Germany, and Israel take advanced placement exams and a third of the students pass. The same article stated that 6.6 percent of U.S. students take advanced placement exams and 4.4 percent pass. Test if the percentage of U.S. students who take advanced placement exams is more than 6.6 percent. State the null and alternative hypotheses. H 0 : p ≤ 0.066 H a : p > 0.066

On a state driver’s test, about 40 percent pass the test on the first try. We want to test if more than 40 percent pass on the first try. Fill in the correct symbol (=, ≠, ≥, <, ≤, >) for the null and alternative hypotheses.

• H 0 : p __ 0.40
• H a : p __ 0.40

Collaborative Exercise

Bring to class a newspaper, some news magazines, and some internet articles. In groups, find articles from which your group can write null and alternative hypotheses. Discuss your hypotheses with the rest of the class.

This book may not be used in the training of large language models or otherwise be ingested into large language models or generative AI offerings without OpenStax's permission.

Want to cite, share, or modify this book? This book uses the Creative Commons Attribution License and you must attribute Texas Education Agency (TEA). The original material is available at: https://www.texasgateway.org/book/tea-statistics . Changes were made to the original material, including updates to art, structure, and other content updates.

Access for free at https://openstax.org/books/statistics/pages/1-introduction

• Authors: Barbara Illowsky, Susan Dean
• Publisher/website: OpenStax
• Book title: Statistics
• Publication date: Mar 27, 2020
• Location: Houston, Texas
• Book URL: https://openstax.org/books/statistics/pages/1-introduction
• Section URL: https://openstax.org/books/statistics/pages/9-1-null-and-alternative-hypotheses

© Apr 16, 2024 Texas Education Agency (TEA). The OpenStax name, OpenStax logo, OpenStax book covers, OpenStax CNX name, and OpenStax CNX logo are not subject to the Creative Commons license and may not be reproduced without the prior and express written consent of Rice University.

• PRO Courses Guides New Tech Help Pro Expert Videos About wikiHow Pro Upgrade Sign In
• EDIT Edit this Article
• EXPLORE Tech Help Pro About Us Random Article Quizzes Request a New Article Community Dashboard This Or That Game Happiness Hub Popular Categories Arts and Entertainment Artwork Books Movies Computers and Electronics Computers Phone Skills Technology Hacks Health Men's Health Mental Health Women's Health Relationships Dating Love Relationship Issues Hobbies and Crafts Crafts Drawing Games Education & Communication Communication Skills Personal Development Studying Personal Care and Style Fashion Hair Care Personal Hygiene Youth Personal Care School Stuff Dating All Categories Arts and Entertainment Finance and Business Home and Garden Relationship Quizzes Cars & Other Vehicles Food and Entertaining Personal Care and Style Sports and Fitness Computers and Electronics Health Pets and Animals Travel Education & Communication Hobbies and Crafts Philosophy and Religion Work World Family Life Holidays and Traditions Relationships Youth
• Browse Articles
• Learn Something New
• Quizzes Hot
• Happiness Hub
• This Or That Game
• Train Your Brain
• Explore More
• Support wikiHow
• About wikiHow
• Log in / Sign up
• Education and Communications
• College University and Postgraduate
• Academic Writing

Writing Null Hypotheses in Research and Statistics

Last Updated: January 17, 2024 Fact Checked

This article was co-authored by Joseph Quinones and by wikiHow staff writer, Jennifer Mueller, JD . Joseph Quinones is a High School Physics Teacher working at South Bronx Community Charter High School. Joseph specializes in astronomy and astrophysics and is interested in science education and science outreach, currently practicing ways to make physics accessible to more students with the goal of bringing more students of color into the STEM fields. He has experience working on Astrophysics research projects at the Museum of Natural History (AMNH). Joseph recieved his Bachelor's degree in Physics from Lehman College and his Masters in Physics Education from City College of New York (CCNY). He is also a member of a network called New York City Men Teach. There are 7 references cited in this article, which can be found at the bottom of the page. This article has been fact-checked, ensuring the accuracy of any cited facts and confirming the authority of its sources. This article has been viewed 28,980 times.

Are you working on a research project and struggling with how to write a null hypothesis? Well, you've come to the right place! Start by recognizing that the basic definition of "null" is "none" or "zero"—that's your biggest clue as to what a null hypothesis should say. Keep reading to learn everything you need to know about the null hypothesis, including how it relates to your research question and your alternative hypothesis as well as how to use it in different types of studies.

Things You Should Know

• Write a research null hypothesis as a statement that the studied variables have no relationship to each other, or that there's no difference between 2 groups.

• Adjust the format of your null hypothesis to match the statistical method you used to test it, such as using "mean" if you're comparing the mean between 2 groups.

What is a null hypothesis?

• Research hypothesis: States in plain language that there's no relationship between the 2 variables or there's no difference between the 2 groups being studied.
• Statistical hypothesis: States the predicted outcome of statistical analysis through a mathematical equation related to the statistical method you're using.

Examples of Null Hypotheses

Null Hypothesis vs. Alternative Hypothesis

• For example, your alternative hypothesis could state a positive correlation between 2 variables while your null hypothesis states there's no relationship. If there's a negative correlation, then both hypotheses are false.

• You need additional data or evidence to show that your alternative hypothesis is correct—proving the null hypothesis false is just the first step.
• In smaller studies, sometimes it's enough to show that there's some relationship and your hypothesis could be correct—you can leave the additional proof as an open question for other researchers to tackle.

How do I test a null hypothesis?

• Group means: Compare the mean of the variable in your sample with the mean of the variable in the general population. [6] X Research source
• Group proportions: Compare the proportion of the variable in your sample with the proportion of the variable in the general population. [7] X Research source
• Correlation: Correlation analysis looks at the relationship between 2 variables—specifically, whether they tend to happen together. [8] X Research source
• Regression: Regression analysis reveals the correlation between 2 variables while also controlling for the effect of other, interrelated variables. [9] X Research source

Templates for Null Hypotheses

• Research null hypothesis: There is no difference in the mean [dependent variable] between [group 1] and [group 2].

• Research null hypothesis: The proportion of [dependent variable] in [group 1] and [group 2] is the same.

• Research null hypothesis: There is no correlation between [independent variable] and [dependent variable] in the population.

• Research null hypothesis: There is no relationship between [independent variable] and [dependent variable] in the population.

Expert Q&A

You Might Also Like

Expert Interview

Thanks for reading our article! If you’d like to learn more about physics, check out our in-depth interview with Joseph Quinones .

• ↑ https://online.stat.psu.edu/stat100/lesson/10/10.1
• ↑ https://online.stat.psu.edu/stat501/lesson/2/2.12
• ↑ https://support.minitab.com/en-us/minitab/21/help-and-how-to/statistics/basic-statistics/supporting-topics/basics/null-and-alternative-hypotheses/
• ↑ https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5635437/
• ↑ https://online.stat.psu.edu/statprogram/reviews/statistical-concepts/hypothesis-testing
• ↑ https://education.arcus.chop.edu/null-hypothesis-testing/
• ↑ https://sphweb.bumc.bu.edu/otlt/mph-modules/bs/bs704_hypothesistest-means-proportions/bs704_hypothesistest-means-proportions_print.html

About This Article

• Send fan mail to authors

Reader Success Stories

Dec 3, 2022

Did this article help you?

Featured Articles

Trending Articles

Watch Articles

• Terms of Use
• Privacy Policy
• Do Not Sell or Share My Info
• Not Selling Info

Get all the best how-tos!

Sign up for wikiHow's weekly email newsletter

What is The Null Hypothesis & When Do You Reject The Null Hypothesis

Julia Simkus

Editor at Simply Psychology

BA (Hons) Psychology, Princeton University

Julia Simkus is a graduate of Princeton University with a Bachelor of Arts in Psychology. She is currently studying for a Master's Degree in Counseling for Mental Health and Wellness in September 2023. Julia's research has been published in peer reviewed journals.

Learn about our Editorial Process

Saul McLeod, PhD

Editor-in-Chief for Simply Psychology

BSc (Hons) Psychology, MRes, PhD, University of Manchester

Saul McLeod, PhD., is a qualified psychology teacher with over 18 years of experience in further and higher education. He has been published in peer-reviewed journals, including the Journal of Clinical Psychology.

Olivia Guy-Evans, MSc

Associate Editor for Simply Psychology

BSc (Hons) Psychology, MSc Psychology of Education

Olivia Guy-Evans is a writer and associate editor for Simply Psychology. She has previously worked in healthcare and educational sectors.

On This Page:

A null hypothesis is a statistical concept suggesting no significant difference or relationship between measured variables. It’s the default assumption unless empirical evidence proves otherwise.

The null hypothesis states no relationship exists between the two variables being studied (i.e., one variable does not affect the other).

The null hypothesis is the statement that a researcher or an investigator wants to disprove.

Testing the null hypothesis can tell you whether your results are due to the effects of manipulating ​ the dependent variable or due to random chance. 

How to Write a Null Hypothesis

Null hypotheses (H0) start as research questions that the investigator rephrases as statements indicating no effect or relationship between the independent and dependent variables.

It is a default position that your research aims to challenge or confirm.

For example, if studying the impact of exercise on weight loss, your null hypothesis might be:

There is no significant difference in weight loss between individuals who exercise daily and those who do not.

Examples of Null Hypotheses

When Do We Reject The Null Hypothesis? 

We reject the null hypothesis when the data provide strong enough evidence to conclude that it is likely incorrect. This often occurs when the p-value (probability of observing the data given the null hypothesis is true) is below a predetermined significance level.

If the collected data does not meet the expectation of the null hypothesis, a researcher can conclude that the data lacks sufficient evidence to back up the null hypothesis, and thus the null hypothesis is rejected. 

Rejecting the null hypothesis means that a relationship does exist between a set of variables and the effect is statistically significant ( p > 0.05).

If the data collected from the random sample is not statistically significance , then the null hypothesis will be accepted, and the researchers can conclude that there is no relationship between the variables. 

You need to perform a statistical test on your data in order to evaluate how consistent it is with the null hypothesis. A p-value is one statistical measurement used to validate a hypothesis against observed data.

Calculating the p-value is a critical part of null-hypothesis significance testing because it quantifies how strongly the sample data contradicts the null hypothesis.

The level of statistical significance is often expressed as a  p  -value between 0 and 1. The smaller the p-value, the stronger the evidence that you should reject the null hypothesis.

Usually, a researcher uses a confidence level of 95% or 99% (p-value of 0.05 or 0.01) as general guidelines to decide if you should reject or keep the null.

When your p-value is less than or equal to your significance level, you reject the null hypothesis.

In other words, smaller p-values are taken as stronger evidence against the null hypothesis. Conversely, when the p-value is greater than your significance level, you fail to reject the null hypothesis.

In this case, the sample data provides insufficient data to conclude that the effect exists in the population.

Because you can never know with complete certainty whether there is an effect in the population, your inferences about a population will sometimes be incorrect.

When you incorrectly reject the null hypothesis, it’s called a type I error. When you incorrectly fail to reject it, it’s called a type II error.

Why Do We Never Accept The Null Hypothesis?

The reason we do not say “accept the null” is because we are always assuming the null hypothesis is true and then conducting a study to see if there is evidence against it. And, even if we don’t find evidence against it, a null hypothesis is not accepted.

A lack of evidence only means that you haven’t proven that something exists. It does not prove that something doesn’t exist. 

It is risky to conclude that the null hypothesis is true merely because we did not find evidence to reject it. It is always possible that researchers elsewhere have disproved the null hypothesis, so we cannot accept it as true, but instead, we state that we failed to reject the null. 

One can either reject the null hypothesis, or fail to reject it, but can never accept it.

Why Do We Use The Null Hypothesis?

We can never prove with 100% certainty that a hypothesis is true; We can only collect evidence that supports a theory. However, testing a hypothesis can set the stage for rejecting or accepting this hypothesis within a certain confidence level.

The null hypothesis is useful because it can tell us whether the results of our study are due to random chance or the manipulation of a variable (with a certain level of confidence).

A null hypothesis is rejected if the measured data is significantly unlikely to have occurred and a null hypothesis is accepted if the observed outcome is consistent with the position held by the null hypothesis.

Rejecting the null hypothesis sets the stage for further experimentation to see if a relationship between two variables exists. 

Hypothesis testing is a critical part of the scientific method as it helps decide whether the results of a research study support a particular theory about a given population. Hypothesis testing is a systematic way of backing up researchers’ predictions with statistical analysis.

It helps provide sufficient statistical evidence that either favors or rejects a certain hypothesis about the population parameter. 

Purpose of a Null Hypothesis 

• The primary purpose of the null hypothesis is to disprove an assumption. 
• Whether rejected or accepted, the null hypothesis can help further progress a theory in many scientific cases.
• A null hypothesis can be used to ascertain how consistent the outcomes of multiple studies are.

Do you always need both a Null Hypothesis and an Alternative Hypothesis?

The null (H0) and alternative (Ha or H1) hypotheses are two competing claims that describe the effect of the independent variable on the dependent variable. They are mutually exclusive, which means that only one of the two hypotheses can be true. 

While the null hypothesis states that there is no effect in the population, an alternative hypothesis states that there is statistical significance between two variables. 

The goal of hypothesis testing is to make inferences about a population based on a sample. In order to undertake hypothesis testing, you must express your research hypothesis as a null and alternative hypothesis. Both hypotheses are required to cover every possible outcome of the study. 

What is the difference between a null hypothesis and an alternative hypothesis?

The alternative hypothesis is the complement to the null hypothesis. The null hypothesis states that there is no effect or no relationship between variables, while the alternative hypothesis claims that there is an effect or relationship in the population.

It is the claim that you expect or hope will be true. The null hypothesis and the alternative hypothesis are always mutually exclusive, meaning that only one can be true at a time.

What are some problems with the null hypothesis?

One major problem with the null hypothesis is that researchers typically will assume that accepting the null is a failure of the experiment. However, accepting or rejecting any hypothesis is a positive result. Even if the null is not refuted, the researchers will still learn something new.

Why can a null hypothesis not be accepted?

We can either reject or fail to reject a null hypothesis, but never accept it. If your test fails to detect an effect, this is not proof that the effect doesn’t exist. It just means that your sample did not have enough evidence to conclude that it exists.

We can’t accept a null hypothesis because a lack of evidence does not prove something that does not exist. Instead, we fail to reject it.

Failing to reject the null indicates that the sample did not provide sufficient enough evidence to conclude that an effect exists.

If the p-value is greater than the significance level, then you fail to reject the null hypothesis.

Is a null hypothesis directional or non-directional?

A hypothesis test can either contain an alternative directional hypothesis or a non-directional alternative hypothesis. A directional hypothesis is one that contains the less than (“<“) or greater than (“>”) sign.

A nondirectional hypothesis contains the not equal sign (“≠”).  However, a null hypothesis is neither directional nor non-directional.

A null hypothesis is a prediction that there will be no change, relationship, or difference between two variables.

The directional hypothesis or nondirectional hypothesis would then be considered alternative hypotheses to the null hypothesis.

Gill, J. (1999). The insignificance of null hypothesis significance testing.  Political research quarterly ,  52 (3), 647-674.

Krueger, J. (2001). Null hypothesis significance testing: On the survival of a flawed method.  American Psychologist ,  56 (1), 16.

Masson, M. E. (2011). A tutorial on a practical Bayesian alternative to null-hypothesis significance testing.  Behavior research methods ,  43 , 679-690.

Nickerson, R. S. (2000). Null hypothesis significance testing: a review of an old and continuing controversy.  Psychological methods ,  5 (2), 241.

Rozeboom, W. W. (1960). The fallacy of the null-hypothesis significance test.  Psychological bulletin ,  57 (5), 416.

Have a language expert improve your writing

Run a free plagiarism check in 10 minutes, generate accurate citations for free.

• Knowledge Base

Methodology

• How to Write a Strong Hypothesis | Steps & Examples

How to Write a Strong Hypothesis | Steps & Examples

Published on May 6, 2022 by Shona McCombes . Revised on November 20, 2023.

A hypothesis is a statement that can be tested by scientific research. If you want to test a relationship between two or more variables, you need to write hypotheses before you start your experiment or data collection .

Example: Hypothesis

Daily apple consumption leads to fewer doctor’s visits.

Table of contents

What is a hypothesis, developing a hypothesis (with example), hypothesis examples, other interesting articles, frequently asked questions about writing hypotheses.

A hypothesis states your predictions about what your research will find. It is a tentative answer to your research question that has not yet been tested. For some research projects, you might have to write several hypotheses that address different aspects of your research question.

A hypothesis is not just a guess – it should be based on existing theories and knowledge. It also has to be testable, which means you can support or refute it through scientific research methods (such as experiments, observations and statistical analysis of data).

Variables in hypotheses

Hypotheses propose a relationship between two or more types of variables .

• An independent variable is something the researcher changes or controls.
• A dependent variable is something the researcher observes and measures.

If there are any control variables , extraneous variables , or confounding variables , be sure to jot those down as you go to minimize the chances that research bias  will affect your results.

In this example, the independent variable is exposure to the sun – the assumed cause . The dependent variable is the level of happiness – the assumed effect .

Receive feedback on language, structure, and formatting

Professional editors proofread and edit your paper by focusing on:

• Academic style
• Vague sentences
• Style consistency

See an example

Step 1. Ask a question

Writing a hypothesis begins with a research question that you want to answer. The question should be focused, specific, and researchable within the constraints of your project.

Step 2. Do some preliminary research

Your initial answer to the question should be based on what is already known about the topic. Look for theories and previous studies to help you form educated assumptions about what your research will find.

At this stage, you might construct a conceptual framework to ensure that you’re embarking on a relevant topic . This can also help you identify which variables you will study and what you think the relationships are between them. Sometimes, you’ll have to operationalize more complex constructs.

Step 3. Formulate your hypothesis

Now you should have some idea of what you expect to find. Write your initial answer to the question in a clear, concise sentence.

4. Refine your hypothesis

You need to make sure your hypothesis is specific and testable. There are various ways of phrasing a hypothesis, but all the terms you use should have clear definitions, and the hypothesis should contain:

• The relevant variables
• The specific group being studied
• The predicted outcome of the experiment or analysis

5. Phrase your hypothesis in three ways

To identify the variables, you can write a simple prediction in  if…then form. The first part of the sentence states the independent variable and the second part states the dependent variable.

In academic research, hypotheses are more commonly phrased in terms of correlations or effects, where you directly state the predicted relationship between variables.

If you are comparing two groups, the hypothesis can state what difference you expect to find between them.

6. Write a null hypothesis

If your research involves statistical hypothesis testing , you will also have to write a null hypothesis . The null hypothesis is the default position that there is no association between the variables. The null hypothesis is written as H 0 , while the alternative hypothesis is H 1 or H a .

• H 0 : The number of lectures attended by first-year students has no effect on their final exam scores.
• H 1 : The number of lectures attended by first-year students has a positive effect on their final exam scores.

If you want to know more about the research process , methodology , research bias , or statistics , make sure to check out some of our other articles with explanations and examples.

• Sampling methods
• Simple random sampling
• Stratified sampling
• Cluster sampling
• Likert scales
• Reproducibility

 Statistics

• Null hypothesis
• Statistical power
• Probability distribution
• Effect size
• Poisson distribution

Research bias

• Optimism bias
• Cognitive bias
• Implicit bias
• Hawthorne effect
• Anchoring bias
• Explicit bias

A hypothesis is not just a guess — it should be based on existing theories and knowledge. It also has to be testable, which means you can support or refute it through scientific research methods (such as experiments, observations and statistical analysis of data).

Null and alternative hypotheses are used in statistical hypothesis testing . The null hypothesis of a test always predicts no effect or no relationship between variables, while the alternative hypothesis states your research prediction of an effect or relationship.

Hypothesis testing is a formal procedure for investigating our ideas about the world using statistics. It is used by scientists to test specific predictions, called hypotheses , by calculating how likely it is that a pattern or relationship between variables could have arisen by chance.

Cite this Scribbr article

If you want to cite this source, you can copy and paste the citation or click the “Cite this Scribbr article” button to automatically add the citation to our free Citation Generator.

McCombes, S. (2023, November 20). How to Write a Strong Hypothesis | Steps & Examples. Scribbr. Retrieved August 26, 2024, from https://www.scribbr.com/methodology/hypothesis/

Is this article helpful?

Shona McCombes

Other students also liked, construct validity | definition, types, & examples, what is a conceptual framework | tips & examples, operationalization | a guide with examples, pros & cons, what is your plagiarism score.

• Science Notes Posts
• Contact Science Notes
• Todd Helmenstine Biography
• Anne Helmenstine Biography
• Free Printable Periodic Tables (PDF and PNG)
• Periodic Table Wallpapers
• Interactive Periodic Table
• Periodic Table Posters
• Science Experiments for Kids
• How to Grow Crystals
• Chemistry Projects
• Fire and Flames Projects
• Holiday Science
• Chemistry Problems With Answers
• Physics Problems
• Unit Conversion Example Problems
• Chemistry Worksheets
• Biology Worksheets
• Periodic Table Worksheets
• Physical Science Worksheets
• Science Lab Worksheets
• My Amazon Books

Null Hypothesis Examples

The null hypothesis (H 0 ) is the hypothesis that states there is no statistical difference between two sample sets. In other words, it assumes the independent variable does not have an effect on the dependent variable in a scientific experiment .

The null hypothesis is the most powerful type of hypothesis in the scientific method because it’s the easiest one to test with a high confidence level using statistics. If the null hypothesis is accepted, then it’s evidence any observed differences between two experiment groups are due to random chance. If the null hypothesis is rejected, then it’s strong evidence there is a true difference between test sets or that the independent variable affects the dependent variable.

• The null hypothesis is a nullifiable hypothesis. A researcher seeks to reject it because this result strongly indicates observed differences are real and not just due to chance.
• The null hypothesis may be accepted or rejected, but not proven. There is always a level of confidence in the outcome.

What Is the Null Hypothesis?

The null hypothesis is written as H 0 , which is read as H-zero, H-nought, or H-null. It is associated with another hypothesis, called the alternate or alternative hypothesis H A or H 1 . When the null hypothesis and alternate hypothesis are written mathematically, they cover all possible outcomes of an experiment.

An experimenter tests the null hypothesis with a statistical analysis called a significance test. The significance test determines the likelihood that the results of the test are not due to chance. Usually, a researcher uses a confidence level of 95% or 99% (p-value of 0.05 or 0.01). But, even if the confidence in the test is high, there is always a small chance the outcome is incorrect. This means you can’t prove a null hypothesis. It’s also a good reason why it’s important to repeat experiments.

Exact and Inexact Null Hypothesis

The most common type of null hypothesis assumes no difference between two samples or groups or no measurable effect of a treatment. This is the exact hypothesis . If you’re asked to state a null hypothesis for a science class, this is the one to write. It is the easiest type of hypothesis to test and is the only one accepted for certain types of analysis. Examples include:

There is no difference between two groups H 0 : μ 1  = μ 2 (where H 0  = the null hypothesis, μ 1  = the mean of population 1, and μ 2  = the mean of population 2)

Both groups have value of 100 (or any number or quality) H 0 : μ = 100

However, sometimes a researcher may test an inexact hypothesis . This type of hypothesis specifies ranges or intervals. Examples include:

Recovery time from a treatment is the same or worse than a placebo: H 0 : μ ≥ placebo time

There is a 5% or less difference between two groups: H 0 : 95 ≤ μ ≤ 105

An inexact hypothesis offers “directionality” about a phenomenon. For example, an exact hypothesis can indicate whether or not a treatment has an effect, while an inexact hypothesis can tell whether an effect is positive of negative. However, an inexact hypothesis may be harder to test and some scientists and statisticians disagree about whether it’s a true null hypothesis .

How to State the Null Hypothesis

To state the null hypothesis, first state what you expect the experiment to show. Then, rephrase the statement in a form that assumes there is no relationship between the variables or that a treatment has no effect.

Example: A researcher tests whether a new drug speeds recovery time from a certain disease. The average recovery time without treatment is 3 weeks.

• State the goal of the experiment: “I hope the average recovery time with the new drug will be less than 3 weeks.”
• Rephrase the hypothesis to assume the treatment has no effect: “If the drug doesn’t shorten recovery time, then the average time will be 3 weeks or longer.” Mathematically: H 0 : μ ≥ 3

This null hypothesis (inexact hypothesis) covers both the scenario in which the drug has no effect and the one in which the drugs makes the recovery time longer. The alternate hypothesis is that average recovery time will be less than three weeks:

H A : μ < 3

Of course, the researcher could test the no-effect hypothesis (exact null hypothesis): H 0 : μ = 3

The danger of testing this hypothesis is that rejecting it only implies the drug affected recovery time (not whether it made it better or worse). This is because the alternate hypothesis is:

H A : μ ≠ 3 (which includes μ <3 and μ >3)

Even though the no-effect null hypothesis yields less information, it’s used because it’s easier to test using statistics. Basically, testing whether something is unchanged/changed is easier than trying to quantify the nature of the change.

Remember, a researcher hopes to reject the null hypothesis because this supports the alternate hypothesis. Also, be sure the null and alternate hypothesis cover all outcomes. Finally, remember a simple true/false, equal/unequal, yes/no exact hypothesis is easier to test than a more complex inexact hypothesis.

• Adèr, H. J.; Mellenbergh, G. J. & Hand, D. J. (2007).  Advising on Research Methods: A Consultant’s Companion . Huizen, The Netherlands: Johannes van Kessel Publishing. ISBN  978-90-79418-01-5 .
• Cox, D. R. (2006).  Principles of Statistical Inference . Cambridge University Press. ISBN  978-0-521-68567-2 .
• Everitt, Brian (1998).  The Cambridge Dictionary of Statistics . Cambridge, UK New York: Cambridge University Press. ISBN 978-0521593465.
• Weiss, Neil A. (1999).  Introductory Statistics  (5th ed.). ISBN 9780201598773.

Related Posts

Have a language expert improve your writing

Run a free plagiarism check in 10 minutes, automatically generate references for free.

• Knowledge Base
• Methodology
• How to Write a Strong Hypothesis | Guide & Examples

How to Write a Strong Hypothesis | Guide & Examples

Published on 6 May 2022 by Shona McCombes .

A hypothesis is a statement that can be tested by scientific research. If you want to test a relationship between two or more variables, you need to write hypotheses before you start your experiment or data collection.

Table of contents

What is a hypothesis, developing a hypothesis (with example), hypothesis examples, frequently asked questions about writing hypotheses.

A hypothesis states your predictions about what your research will find. It is a tentative answer to your research question that has not yet been tested. For some research projects, you might have to write several hypotheses that address different aspects of your research question.

A hypothesis is not just a guess – it should be based on existing theories and knowledge. It also has to be testable, which means you can support or refute it through scientific research methods (such as experiments, observations, and statistical analysis of data).

Variables in hypotheses

Hypotheses propose a relationship between two or more variables . An independent variable is something the researcher changes or controls. A dependent variable is something the researcher observes and measures.

In this example, the independent variable is exposure to the sun – the assumed cause . The dependent variable is the level of happiness – the assumed effect .

Prevent plagiarism, run a free check.

Step 1: ask a question.

Writing a hypothesis begins with a research question that you want to answer. The question should be focused, specific, and researchable within the constraints of your project.

Step 2: Do some preliminary research

Your initial answer to the question should be based on what is already known about the topic. Look for theories and previous studies to help you form educated assumptions about what your research will find.

At this stage, you might construct a conceptual framework to identify which variables you will study and what you think the relationships are between them. Sometimes, you’ll have to operationalise more complex constructs.

Step 3: Formulate your hypothesis

Now you should have some idea of what you expect to find. Write your initial answer to the question in a clear, concise sentence.

Step 4: Refine your hypothesis

You need to make sure your hypothesis is specific and testable. There are various ways of phrasing a hypothesis, but all the terms you use should have clear definitions, and the hypothesis should contain:

• The relevant variables
• The specific group being studied
• The predicted outcome of the experiment or analysis

Step 5: Phrase your hypothesis in three ways

To identify the variables, you can write a simple prediction in if … then form. The first part of the sentence states the independent variable and the second part states the dependent variable.

In academic research, hypotheses are more commonly phrased in terms of correlations or effects, where you directly state the predicted relationship between variables.

If you are comparing two groups, the hypothesis can state what difference you expect to find between them.

Step 6. Write a null hypothesis

If your research involves statistical hypothesis testing , you will also have to write a null hypothesis. The null hypothesis is the default position that there is no association between the variables. The null hypothesis is written as H 0 , while the alternative hypothesis is H 1 or H a .

Hypothesis testing is a formal procedure for investigating our ideas about the world using statistics. It is used by scientists to test specific predictions, called hypotheses , by calculating how likely it is that a pattern or relationship between variables could have arisen by chance.

A hypothesis is not just a guess. It should be based on existing theories and knowledge. It also has to be testable, which means you can support or refute it through scientific research methods (such as experiments, observations, and statistical analysis of data).

A research hypothesis is your proposed answer to your research question. The research hypothesis usually includes an explanation (‘ x affects y because …’).

A statistical hypothesis, on the other hand, is a mathematical statement about a population parameter. Statistical hypotheses always come in pairs: the null and alternative hypotheses. In a well-designed study , the statistical hypotheses correspond logically to the research hypothesis.

Cite this Scribbr article

If you want to cite this source, you can copy and paste the citation or click the ‘Cite this Scribbr article’ button to automatically add the citation to our free Reference Generator.

McCombes, S. (2022, May 06). How to Write a Strong Hypothesis | Guide & Examples. Scribbr. Retrieved 26 August 2024, from https://www.scribbr.co.uk/research-methods/hypothesis-writing/

Is this article helpful?

Shona McCombes

Other students also liked, operationalisation | a guide with examples, pros & cons, what is a conceptual framework | tips & examples, a quick guide to experimental design | 5 steps & examples.

Module 9: Hypothesis Testing With One Sample

Null and alternative hypotheses, learning outcomes.

• Describe hypothesis testing in general and in practice

The actual test begins by considering two  hypotheses . They are called the null hypothesis and the alternative hypothesis . These hypotheses contain opposing viewpoints.

H 0 : The null hypothesis: It is a statement about the population that either is believed to be true or is used to put forth an argument unless it can be shown to be incorrect beyond a reasonable doubt.

H a : The alternative hypothesis : It is a claim about the population that is contradictory to H 0 and what we conclude when we reject H 0 .

Since the null and alternative hypotheses are contradictory, you must examine evidence to decide if you have enough evidence to reject the null hypothesis or not. The evidence is in the form of sample data.

After you have determined which hypothesis the sample supports, you make adecision. There are two options for a  decision . They are “reject H 0 ” if the sample information favors the alternative hypothesis or “do not reject H 0 ” or “decline to reject H 0 ” if the sample information is insufficient to reject the null hypothesis.

Mathematical Symbols Used in  H 0 and H a :

H 0 always has a symbol with an equal in it. H a never has a symbol with an equal in it. The choice of symbol depends on the wording of the hypothesis test. However, be aware that many researchers (including one of the co-authors in research work) use = in the null hypothesis, even with > or < as the symbol in the alternative hypothesis. This practice is acceptable because we only make the decision to reject or not reject the null hypothesis.

H 0 : No more than 30% of the registered voters in Santa Clara County voted in the primary election. p ≤ 30

H a : More than 30% of the registered voters in Santa Clara County voted in the primary election. p > 30

A medical trial is conducted to test whether or not a new medicine reduces cholesterol by 25%. State the null and alternative hypotheses.

H 0 : The drug reduces cholesterol by 25%. p = 0.25

H a : The drug does not reduce cholesterol by 25%. p ≠ 0.25

We want to test whether the mean GPA of students in American colleges is different from 2.0 (out of 4.0). The null and alternative hypotheses are:

H 0 : μ = 2.0

H a : μ ≠ 2.0

We want to test whether the mean height of eighth graders is 66 inches. State the null and alternative hypotheses. Fill in the correct symbol (=, ≠, ≥, <, ≤, >) for the null and alternative hypotheses. H 0 : μ __ 66 H a : μ __ 66

• H 0 : μ = 66
• H a : μ ≠ 66

We want to test if college students take less than five years to graduate from college, on the average. The null and alternative hypotheses are:

H 0 : μ ≥ 5

H a : μ < 5

We want to test if it takes fewer than 45 minutes to teach a lesson plan. State the null and alternative hypotheses. Fill in the correct symbol ( =, ≠, ≥, <, ≤, >) for the null and alternative hypotheses. H 0 : μ __ 45 H a : μ __ 45

• H 0 : μ ≥ 45
• H a : μ < 45

In an issue of U.S. News and World Report , an article on school standards stated that about half of all students in France, Germany, and Israel take advanced placement exams and a third pass. The same article stated that 6.6% of U.S. students take advanced placement exams and 4.4% pass. Test if the percentage of U.S. students who take advanced placement exams is more than 6.6%. State the null and alternative hypotheses.

H 0 : p ≤ 0.066

H a : p > 0.066

On a state driver’s test, about 40% pass the test on the first try. We want to test if more than 40% pass on the first try. Fill in the correct symbol (=, ≠, ≥, <, ≤, >) for the null and alternative hypotheses. H 0 : p __ 0.40 H a : p __ 0.40

• H 0 : p = 0.40
• H a : p > 0.40

Concept Review

In a  hypothesis test , sample data is evaluated in order to arrive at a decision about some type of claim. If certain conditions about the sample are satisfied, then the claim can be evaluated for a population. In a hypothesis test, we: Evaluate the null hypothesis , typically denoted with H 0 . The null is not rejected unless the hypothesis test shows otherwise. The null statement must always contain some form of equality (=, ≤ or ≥) Always write the alternative hypothesis , typically denoted with H a or H 1 , using less than, greater than, or not equals symbols, i.e., (≠, >, or <). If we reject the null hypothesis, then we can assume there is enough evidence to support the alternative hypothesis. Never state that a claim is proven true or false. Keep in mind the underlying fact that hypothesis testing is based on probability laws; therefore, we can talk only in terms of non-absolute certainties.

Formula Review

H 0 and H a are contradictory.

• OpenStax, Statistics, Null and Alternative Hypotheses. Provided by : OpenStax. Located at : http://cnx.org/contents/[email protected]:58/Introductory_Statistics . License : CC BY: Attribution
• Introductory Statistics . Authored by : Barbara Illowski, Susan Dean. Provided by : Open Stax. Located at : http://cnx.org/contents/[email protected] . License : CC BY: Attribution . License Terms : Download for free at http://cnx.org/contents/[email protected]
• Simple hypothesis testing | Probability and Statistics | Khan Academy. Authored by : Khan Academy. Located at : https://youtu.be/5D1gV37bKXY . License : All Rights Reserved . License Terms : Standard YouTube License

Null Hypothesis Definition and Examples, How to State

What is the null hypothesis, how to state the null hypothesis, null hypothesis overview.

Why is it Called the “Null”?

The word “null” in this context means that it’s a commonly accepted fact that researchers work to nullify . It doesn’t mean that the statement is null (i.e. amounts to nothing) itself! (Perhaps the term should be called the “nullifiable hypothesis” as that might cause less confusion).

Why Do I need to Test it? Why not just prove an alternate one?

The short answer is, as a scientist, you are required to ; It’s part of the scientific process. Science uses a battery of processes to prove or disprove theories, making sure than any new hypothesis has no flaws. Including both a null and an alternate hypothesis is one safeguard to ensure your research isn’t flawed. Not including the null hypothesis in your research is considered very bad practice by the scientific community. If you set out to prove an alternate hypothesis without considering it, you are likely setting yourself up for failure. At a minimum, your experiment will likely not be taken seriously.

• Null hypothesis : H 0 : The world is flat.
• Alternate hypothesis: The world is round.

Several scientists, including Copernicus , set out to disprove the null hypothesis. This eventually led to the rejection of the null and the acceptance of the alternate. Most people accepted it — the ones that didn’t created the Flat Earth Society !. What would have happened if Copernicus had not disproved the it and merely proved the alternate? No one would have listened to him. In order to change people’s thinking, he first had to prove that their thinking was wrong .

How to State the Null Hypothesis from a Word Problem

You’ll be asked to convert a word problem into a hypothesis statement in statistics that will include a null hypothesis and an alternate hypothesis . Breaking your problem into a few small steps makes these problems much easier to handle.

Step 2: Convert the hypothesis to math . Remember that the average is sometimes written as μ.

H 1 : μ > 8.2

Broken down into (somewhat) English, that’s H 1 (The hypothesis): μ (the average) > (is greater than) 8.2

Step 3: State what will happen if the hypothesis doesn’t come true. If the recovery time isn’t greater than 8.2 weeks, there are only two possibilities, that the recovery time is equal to 8.2 weeks or less than 8.2 weeks.

H 0 : μ ≤ 8.2

Broken down again into English, that’s H 0 (The null hypothesis): μ (the average) ≤ (is less than or equal to) 8.2

How to State the Null Hypothesis: Part Two

But what if the researcher doesn’t have any idea what will happen.

Example Problem: A researcher is studying the effects of radical exercise program on knee surgery patients. There is a good chance the therapy will improve recovery time, but there’s also the possibility it will make it worse. Average recovery times for knee surgery patients is 8.2 weeks. 

Step 1: State what will happen if the experiment doesn’t make any difference. That’s the null hypothesis–that nothing will happen. In this experiment, if nothing happens, then the recovery time will stay at 8.2 weeks.

H 0 : μ = 8.2

Broken down into English, that’s H 0 (The null hypothesis): μ (the average) = (is equal to) 8.2

Step 2: Figure out the alternate hypothesis . The alternate hypothesis is the opposite of the null hypothesis. In other words, what happens if our experiment makes a difference?

H 1 : μ ≠ 8.2

In English again, that’s H 1 (The  alternate hypothesis): μ (the average) ≠ (is not equal to) 8.2

That’s How to State the Null Hypothesis!

Check out our Youtube channel for more stats tips!

Gonick, L. (1993). The Cartoon Guide to Statistics . HarperPerennial. Kotz, S.; et al., eds. (2006), Encyclopedia of Statistical Sciences , Wiley.

Null Hypothesis Definition and Examples

PM Images / Getty Images

• Chemical Laws
• Periodic Table
• Projects & Experiments
• Scientific Method
• Biochemistry
• Physical Chemistry
• Medical Chemistry
• Chemistry In Everyday Life
• Famous Chemists
• Activities for Kids
• Abbreviations & Acronyms
• Weather & Climate
• Ph.D., Biomedical Sciences, University of Tennessee at Knoxville
• B.A., Physics and Mathematics, Hastings College

In a scientific experiment, the null hypothesis is the proposition that there is no effect or no relationship between phenomena or populations. If the null hypothesis is true, any observed difference in phenomena or populations would be due to sampling error (random chance) or experimental error. The null hypothesis is useful because it can be tested and found to be false, which then implies that there is a relationship between the observed data. It may be easier to think of it as a nullifiable hypothesis or one that the researcher seeks to nullify. The null hypothesis is also known as the H 0, or no-difference hypothesis.

The alternate hypothesis, H A or H 1 , proposes that observations are influenced by a non-random factor. In an experiment, the alternate hypothesis suggests that the experimental or independent variable has an effect on the dependent variable .

How to State a Null Hypothesis

There are two ways to state a null hypothesis. One is to state it as a declarative sentence, and the other is to present it as a mathematical statement.

For example, say a researcher suspects that exercise is correlated to weight loss, assuming diet remains unchanged. The average length of time to achieve a certain amount of weight loss is six weeks when a person works out five times a week. The researcher wants to test whether weight loss takes longer to occur if the number of workouts is reduced to three times a week.

The first step to writing the null hypothesis is to find the (alternate) hypothesis. In a word problem like this, you're looking for what you expect to be the outcome of the experiment. In this case, the hypothesis is "I expect weight loss to take longer than six weeks."

This can be written mathematically as: H 1 : μ > 6

In this example, μ is the average.

Now, the null hypothesis is what you expect if this hypothesis does not happen. In this case, if weight loss isn't achieved in greater than six weeks, then it must occur at a time equal to or less than six weeks. This can be written mathematically as:

H 0 : μ ≤ 6

The other way to state the null hypothesis is to make no assumption about the outcome of the experiment. In this case, the null hypothesis is simply that the treatment or change will have no effect on the outcome of the experiment. For this example, it would be that reducing the number of workouts would not affect the time needed to achieve weight loss:

H 0 : μ = 6

Null Hypothesis Examples

"Hyperactivity is unrelated to eating sugar " is an example of a null hypothesis. If the hypothesis is tested and found to be false, using statistics, then a connection between hyperactivity and sugar ingestion may be indicated. A significance test is the most common statistical test used to establish confidence in a null hypothesis.

Another example of a null hypothesis is "Plant growth rate is unaffected by the presence of cadmium in the soil ." A researcher could test the hypothesis by measuring the growth rate of plants grown in a medium lacking cadmium, compared with the growth rate of plants grown in mediums containing different amounts of cadmium. Disproving the null hypothesis would set the groundwork for further research into the effects of different concentrations of the element in soil.

Why Test a Null Hypothesis?

You may be wondering why you would want to test a hypothesis just to find it false. Why not just test an alternate hypothesis and find it true? The short answer is that it is part of the scientific method. In science, propositions are not explicitly "proven." Rather, science uses math to determine the probability that a statement is true or false. It turns out it's much easier to disprove a hypothesis than to positively prove one. Also, while the null hypothesis may be simply stated, there's a good chance the alternate hypothesis is incorrect.

For example, if your null hypothesis is that plant growth is unaffected by duration of sunlight, you could state the alternate hypothesis in several different ways. Some of these statements might be incorrect. You could say plants are harmed by more than 12 hours of sunlight or that plants need at least three hours of sunlight, etc. There are clear exceptions to those alternate hypotheses, so if you test the wrong plants, you could reach the wrong conclusion. The null hypothesis is a general statement that can be used to develop an alternate hypothesis, which may or may not be correct.

• Kelvin Temperature Scale Definition
• Independent Variable Definition and Examples
• Theory Definition in Science
• Hypothesis Definition (Science)
• de Broglie Equation Definition
• Law of Combining Volumes Definition
• Chemical Definition
• Pure Substance Definition in Chemistry
• Acid Definition and Examples
• Extensive Property Definition (Chemistry)
• Radiation Definition and Examples
• Valence Definition in Chemistry
• Atomic Solid Definition
• Weak Base Definition and Examples
• Oxidation Definition and Example in Chemistry
• Definition of Binary Compound

User Preferences

Content preview.

Arcu felis bibendum ut tristique et egestas quis:

• Ut enim ad minim veniam, quis nostrud exercitation ullamco laboris
• Duis aute irure dolor in reprehenderit in voluptate
• Excepteur sint occaecat cupidatat non proident

Keyboard Shortcuts

10.1 - setting the hypotheses: examples.

A significance test examines whether the null hypothesis provides a plausible explanation of the data. The null hypothesis itself does not involve the data. It is a statement about a parameter (a numerical characteristic of the population). These population values might be proportions or means or differences between means or proportions or correlations or odds ratios or any other numerical summary of the population. The alternative hypothesis is typically the research hypothesis of interest. Here are some examples.

Example 10.2: Hypotheses with One Sample of One Categorical Variable Section  

About 10% of the human population is left-handed. Suppose a researcher at Penn State speculates that students in the College of Arts and Architecture are more likely to be left-handed than people found in the general population. We only have one sample since we will be comparing a population proportion based on a sample value to a known population value.

• Research Question : Are artists more likely to be left-handed than people found in the general population?
• Response Variable : Classification of the student as either right-handed or left-handed

State Null and Alternative Hypotheses

• Null Hypothesis : Students in the College of Arts and Architecture are no more likely to be left-handed than people in the general population (population percent of left-handed students in the College of Art and Architecture = 10% or p = .10).
• Alternative Hypothesis : Students in the College of Arts and Architecture are more likely to be left-handed than people in the general population (population percent of left-handed students in the College of Arts and Architecture > 10% or p > .10). This is a one-sided alternative hypothesis.

Example 10.3: Hypotheses with One Sample of One Measurement Variable Section  

A generic brand of the anti-histamine Diphenhydramine markets a capsule with a 50 milligram dose. The manufacturer is worried that the machine that fills the capsules has come out of calibration and is no longer creating capsules with the appropriate dosage.

• Research Question : Does the data suggest that the population mean dosage of this brand is different than 50 mg?
• Response Variable : dosage of the active ingredient found by a chemical assay.
• Null Hypothesis : On the average, the dosage sold under this brand is 50 mg (population mean dosage = 50 mg).
• Alternative Hypothesis : On the average, the dosage sold under this brand is not 50 mg (population mean dosage ≠ 50 mg). This is a two-sided alternative hypothesis.

Example 10.4: Hypotheses with Two Samples of One Categorical Variable Section  

Many people are starting to prefer vegetarian meals on a regular basis. Specifically, a researcher believes that females are more likely than males to eat vegetarian meals on a regular basis.

• Research Question : Does the data suggest that females are more likely than males to eat vegetarian meals on a regular basis?
• Response Variable : Classification of whether or not a person eats vegetarian meals on a regular basis
• Explanatory (Grouping) Variable: Sex
• Null Hypothesis : There is no sex effect regarding those who eat vegetarian meals on a regular basis (population percent of females who eat vegetarian meals on a regular basis = population percent of males who eat vegetarian meals on a regular basis or p females = p males ).
• Alternative Hypothesis : Females are more likely than males to eat vegetarian meals on a regular basis (population percent of females who eat vegetarian meals on a regular basis > population percent of males who eat vegetarian meals on a regular basis or p females > p males ). This is a one-sided alternative hypothesis.

Example 10.5: Hypotheses with Two Samples of One Measurement Variable Section  

Obesity is a major health problem today. Research is starting to show that people may be able to lose more weight on a low carbohydrate diet than on a low fat diet.

• Research Question : Does the data suggest that, on the average, people are able to lose more weight on a low carbohydrate diet than on a low fat diet?
• Response Variable : Weight loss (pounds)
• Explanatory (Grouping) Variable : Type of diet
• Null Hypothesis : There is no difference in the mean amount of weight loss when comparing a low carbohydrate diet with a low fat diet (population mean weight loss on a low carbohydrate diet = population mean weight loss on a low fat diet).
• Alternative Hypothesis : The mean weight loss should be greater for those on a low carbohydrate diet when compared with those on a low fat diet (population mean weight loss on a low carbohydrate diet > population mean weight loss on a low fat diet). This is a one-sided alternative hypothesis.

Example 10.6: Hypotheses about the relationship between Two Categorical Variables Section  

• Research Question : Do the odds of having a stroke increase if you inhale second hand smoke ? A case-control study of non-smoking stroke patients and controls of the same age and occupation are asked if someone in their household smokes.
• Variables : There are two different categorical variables (Stroke patient vs control and whether the subject lives in the same household as a smoker). Living with a smoker (or not) is the natural explanatory variable and having a stroke (or not) is the natural response variable in this situation.
• Null Hypothesis : There is no relationship between whether or not a person has a stroke and whether or not a person lives with a smoker (odds ratio between stroke and second-hand smoke situation is = 1).
• Alternative Hypothesis : There is a relationship between whether or not a person has a stroke and whether or not a person lives with a smoker (odds ratio between stroke and second-hand smoke situation is > 1). This is a one-tailed alternative.

This research question might also be addressed like example 11.4 by making the hypotheses about comparing the proportion of stroke patients that live with smokers to the proportion of controls that live with smokers.

Example 10.7: Hypotheses about the relationship between Two Measurement Variables Section  

• Research Question : A financial analyst believes there might be a positive association between the change in a stock's price and the amount of the stock purchased by non-management employees the previous day (stock trading by management being under "insider-trading" regulatory restrictions).
• Variables : Daily price change information (the response variable) and previous day stock purchases by non-management employees (explanatory variable). These are two different measurement variables.
• Null Hypothesis : The correlation between the daily stock price change (\$) and the daily stock purchases by non-management employees (\$) = 0.
• Alternative Hypothesis : The correlation between the daily stock price change (\$) and the daily stock purchases by non-management employees (\$) > 0. This is a one-sided alternative hypothesis.

Example 10.8: Hypotheses about comparing the relationship between Two Measurement Variables in Two Samples Section  

• Research Question : Is there a linear relationship between the amount of the bill (\$) at a restaurant and the tip (\$) that was left. Is the strength of this association different for family restaurants than for fine dining restaurants?
• Variables : There are two different measurement variables. The size of the tip would depend on the size of the bill so the amount of the bill would be the explanatory variable and the size of the tip would be the response variable.
• Null Hypothesis : The correlation between the amount of the bill (\$) at a restaurant and the tip (\$) that was left is the same at family restaurants as it is at fine dining restaurants.
• Alternative Hypothesis : The correlation between the amount of the bill (\$) at a restaurant and the tip (\$) that was left is the difference at family restaurants then it is at fine dining restaurants. This is a two-sided alternative hypothesis.

• Null hypothesis

by Marco Taboga , PhD

In a test of hypothesis , a sample of data is used to decide whether to reject or not to reject a hypothesis about the probability distribution from which the sample was extracted.

The hypothesis is called the null hypothesis, or simply "the null".

Table of contents

The null is like the defendant in a criminal trial

How is the null hypothesis tested, example 1 - proportion of defective items, measurement, test statistic, critical region, interpretation, example 2 - reliability of a production plant, rejection and failure to reject, not rejecting and accepting are not the same thing, failure to reject can be due to lack of power, rejections are easier to interpret, but be careful, takeaways - how to (and not to) formulate a null hypothesis, more examples, more details, best practices in science, keep reading the glossary.

Formulating null hypotheses and subjecting them to statistical testing is one of the workhorses of the scientific method.

Scientists in all fields make conjectures about the phenomena they study, translate them into null hypotheses and gather data to test them.

This process resembles a trial:

the defendant (the null hypothesis) is accused of being guilty (wrong);

evidence (data) is gathered in order to prove the defendant guilty (reject the null);

if there is evidence beyond any reasonable doubt, the defendant is found guilty (the null is rejected);

otherwise, the defendant is found not guilty (the null is not rejected).

Keep this analogy in mind because it helps to better understand statistical tests, their limitations, use and misuse, and frequent misinterpretation.

Before collecting the data:

we decide how to summarize the relevant characteristics of the sample data in a single number, the so-called test statistic ;

we derive the probability distribution of the test statistic under the hypothesis that the null is true (the data is regarded as random; therefore, the test statistic is a random variable);

we decide what probability of incorrectly rejecting the null we are willing to tolerate (the level of significance , or size of the test ); the level of significance is typically a small number, such as 5% or 1%.

we choose one or more intervals of values (collectively called rejection region) such that the probability that the test statistic falls within these intervals is equal to the desired level of significance; the rejection region is often a tail of the distribution of the test statistic (one-tailed test) or the union of the left and right tails (two-tailed test).

Then, the data is collected and used to compute the value of the test statistic.

A decision is taken as follows:

if the test statistic falls within the rejection region, then the null hypothesis is rejected;

otherwise, it is not rejected.

We now make two examples of practical problems that lead to formulate and test a null hypothesis.

A new method is proposed to produce light bulbs.

The proponents claim that it produces less defective bulbs than the method currently in use.

To check the claim, we can set up a statistical test as follows.

We keep the light bulbs on for 10 consecutive days, and then we record whether they are still working at the end of the test period.

The probability that a light bulb produced with the new method is still working at the end of the test period is the same as that of a light bulb produced with the old method.

100 light bulbs are tested:

50 of them are produced with the new method (group A)

the remaining 50 are produced with the old method (group B).

The final data comprises 100 observations of:

an indicator variable which is equal to 1 if the light bulb is still working at the end of the test period and 0 otherwise;

a categorical variable that records the group (A or B) to which each light bulb belongs.

We use the data to compute the proportions of working light bulbs in groups A and B.

The proportions are estimates of the probabilities of not being defective, which are equal for the two groups under the null hypothesis.

We then compute a z-statistic (see here for details) by:

taking the difference between the proportion in group A and the proportion in group B;

standardizing the difference:

we subtract the expected value (which is zero under the null hypothesis);

we divide by the standard deviation (it can be derived analytically).

The distribution of the z-statistic can be approximated by a standard normal distribution .

We decide that the level of confidence must be 5%. In other words, we are going to tolerate a 5% probability of incorrectly rejecting the null hypothesis.

The critical region is the right 5%-tail of the normal distribution, that is, the set of all values greater than 1.645 (see the glossary entry on critical values if you are wondering how this value was obtained).

If the test statistic is greater than 1.645, then the null hypothesis is rejected; otherwise, it is not rejected.

A rejection is interpreted as significant evidence that the new production method produces less defective items; failure to reject is interpreted as insufficient evidence that the new method is better.

A production plant incurs high costs when production needs to be halted because some machinery fails.

The plant manager has decided that he is not willing to tolerate more than one halt per year on average.

If the expected number of halts per year is greater than 1, he will make new investments in order to improve the reliability of the plant.

A statistical test is set up as follows.

The reliability of the plant is measured by the number of halts.

The number of halts in a year is assumed to have a Poisson distribution with expected value equal to 1 (using the Poisson distribution is common in reliability testing).

The manager cannot wait more than one year before taking a decision.

There will be a single datum at his disposal: the number of halts observed during one year.

The number of halts is used as a test statistic. By assumption, it has a Poisson distribution under the null hypothesis.

The manager decides that the probability of incorrectly rejecting the null can be at most 10%.

A Poisson random variable with expected value equal to 1 takes values:

larger than 1 with probability 26.42%;

larger than 2 with probability 8.03%.

Therefore, it is decided that the critical region will be the set of all values greater than or equal to 3.

If the test statistic is strictly greater than or equal to 3, then the null is rejected; otherwise, it is not rejected.

A rejection is interpreted as significant evidence that the production plant is not reliable enough (the average number of halts per year is significantly larger than tolerated).

Failure to reject is interpreted as insufficient evidence that the plant is unreliable.

This section discusses the main problems that arise in the interpretation of the outcome of a statistical test (reject / not reject).

When the test statistic does not fall within the critical region, then we do not reject the null hypothesis.

Does this mean that we accept the null? Not really.

In general, failure to reject does not constitute, per se, strong evidence that the null hypothesis is true .

Remember the analogy between hypothesis testing and a criminal trial. In a trial, when the defendant is declared not guilty, this does not mean that the defendant is innocent. It only means that there was not enough evidence (not beyond any reasonable doubt) against the defendant.

In turn, lack of evidence can be due:

either to the fact that the defendant is innocent ;

or to the fact that the prosecution has not been able to provide enough evidence against the defendant, even if the latter is guilty .

This is the very reason why courts do not declare defendants innocent, but they use the locution "not guilty".

In a similar fashion, statisticians do not say that the null hypothesis has been accepted, but they say that it has not been rejected.

To better understand why failure to reject does not in general constitute strong evidence that the null hypothesis is true, we need to use the concept of statistical power .

The power of a test is the probability (calculated ex-ante, i.e., before observing the data) that the null will be rejected when another hypothesis (called the alternative hypothesis ) is true.

Let's consider the first of the two examples above (the production of light bulbs).

In that example, the null hypothesis is: the probability that a light bulb is defective does not decrease after introducing a new production method.

Let's make the alternative hypothesis that the probability of being defective is 1% smaller after changing the production process (assume that a 1% decrease is considered a meaningful improvement by engineers).

How much is the ex-ante probability of rejecting the null if the alternative hypothesis is true?

If this probability (the power of the test) is small, then it is very likely that we will not reject the null even if it is wrong.

If we use the analogy with criminal trials, low power means that most likely the prosecution will not be able to provide sufficient evidence, even if the defendant is guilty.

Thus, in the case of lack of power, failure to reject is almost meaningless (it was anyway highly likely).

This is why, before performing a test, it is good statistical practice to compute its power against a relevant alternative .

If the power is found to be too small, there are usually remedies. In particular, statistical power can usually be increased by increasing the sample size (see, e.g., the lecture on hypothesis tests about the mean ).

As we have explained above, interpreting a failure to reject the null hypothesis is not always straightforward. Instead, interpreting a rejection is somewhat easier.

When we reject the null, we know that the data has provided a lot of evidence against the null. In other words, it is unlikely (how unlikely depends on the size of the test) that the null is true given the data we have observed.

There is an important caveat though. The null hypothesis is often made up of several assumptions, including:

the main assumption (the one we are testing);

other assumptions (e.g., technical assumptions) that we need to make in order to set up the hypothesis test.

For instance, in Example 2 above (reliability of a production plant), the main assumption is that the expected number of production halts per year is equal to 1. But there is also a technical assumption: the number of production halts has a Poisson distribution.

It must be kept in mind that a rejection is always a joint rejection of the main assumption and all the other assumptions .

Therefore, we should always ask ourselves whether the null has been rejected because the main assumption is wrong or because the other assumptions are violated.

In the case of Example 2 above, is a rejection of the null due to the fact that the expected number of halts is greater than 1 or is it due to the fact that the distribution of the number of halts is very different from a Poisson distribution?

When we suspect that a rejection is due to the inappropriateness of some technical assumption (e.g., assuming a Poisson distribution in the example), we say that the rejection could be due to misspecification of the model .

The right thing to do when these kind of suspicions arise is to conduct so-called robustness checks , that is, to change the technical assumptions and carry out the test again.

In our example, we could re-run the test by assuming a different probability distribution for the number of halts (e.g., a negative binomial or a compound Poisson - do not worry if you have never heard about these distributions).

If we keep obtaining a rejection of the null even after changing the technical assumptions several times, the we say that our rejection is robust to several different specifications of the model .

What are the main practical implications of everything we have said thus far? How does the theory above help us to set up and test a null hypothesis?

What we said can be summarized in the following guiding principles:

A test of hypothesis is like a criminal trial and you are the prosecutor . You want to find evidence that the defendant (the null hypothesis) is guilty. Your job is not to prove that the defendant is innocent. If you find yourself hoping that the defendant is found not guilty (i.e., the null is not rejected) then something is wrong with the way you set up the test. Remember: you are the prosecutor.

Compute the power of your test against one or more relevant alternative hypotheses. Do not run a test if you know ex-ante that it is unlikely to reject the null when the alternative hypothesis is true.

Beware of technical assumptions that you add to the main assumption you want to test. Make robustness checks in order to verify that the outcome of the test is not biased by model misspecification.

More examples of null hypotheses and how to test them can be found in the following lectures.

The lecture on Hypothesis testing provides a more detailed mathematical treatment of null hypotheses and how they are tested.

This lecture on the null hypothesis was featured in Stanford University's Best practices in science .

Previous entry: Normal equations

Next entry: Parameter

How to cite

Please cite as:

Taboga, Marco (2021). "Null hypothesis", Lectures on probability theory and mathematical statistics. Kindle Direct Publishing. Online appendix. https://www.statlect.com/glossary/null-hypothesis.

Most of the learning materials found on this website are now available in a traditional textbook format.

• Permutations
• Characteristic function
• Almost sure convergence
• Likelihood ratio test
• Uniform distribution
• Bernoulli distribution
• Multivariate normal distribution
• Chi-square distribution
• Maximum likelihood
• Mathematical tools
• Fundamentals of probability
• Probability distributions
• Asymptotic theory
• Fundamentals of statistics
• About Statlect
• Cookies, privacy and terms of use
• Precision matrix
• Distribution function
• Mean squared error
• IID sequence
• To enhance your privacy,
• we removed the social buttons,
• but don't forget to share .

15 Null Hypothesis Examples

Chris Drew (PhD)

Dr. Chris Drew is the founder of the Helpful Professor. He holds a PhD in education and has published over 20 articles in scholarly journals. He is the former editor of the Journal of Learning Development in Higher Education. [Image Descriptor: Photo of Chris]

Learn about our Editorial Process

A null hypothesis is a general assertion or default position that there is no relationship or effect between two measured phenomena.

It’s a critical part of statistics, data analysis, and the scientific method . This concept forms the basis of testing statistical significance and allows researchers to be objective in their conclusions.

A null hypothesis helps to eliminate biases and ensures that the observed results are not due to chance. The rejection or failure to reject the null hypothesis helps in guiding the course of research.

Null Hypothesis Definition

The null hypothesis, often denoted as H 0 , is the hypothesis in a statistical test which proposes no statistical significance exists in a set of observed data.

It hypothesizes that any kind of difference or importance you see in a data set is due to chance.

Null hypotheses are typically proposed to be negated or disproved by statistical tests, paving way for the acceptance of an alternate hypothesis.

Importantly, a null hypothesis cannot be proven true; it can only be supported or rejected with confidence.

Should evidence – via statistical analysis – contradict the null hypothesis, it is rejected in favor of an alternative hypothesis. In essence, the null hypothesis is a tool to challenge and disprove that there is no effect or relationship between variables.

Video Explanation

I like to show this video to my students which outlines a null hypothesis really clearly and engagingly, using real life studies by research students! The into explains it really well:

“There’s an idea in science called the null hypothesis and it works like this: when you’re setting out to prove a theory, your default answer should be “it’s not going to work” and you have to convince the world otherwise through clear results”

Here’s the full video:

Null Hypothesis Examples

• Equality of Means: The null hypothesis posits that the average of group A does not differ from the average of group B. It suggests that any observed difference between the two group means is due to sampling or experimental error.
• No Correlation: The null hypothesis states there is no correlation between the variable X and variable Y in the population. It means that any correlation seen in sample data occurred by chance.
• Drug Effectiveness: The null hypothesis proposes that a new drug does not reduce the number of days to recover from a disease compared to a standard drug. Any observed difference is merely by chance and not due to the new drug.
• Classroom Teaching Method: The null hypothesis states that a new teaching method does not result in improved test scores compared to the traditional teaching method. Any improvement in scores can be attributed to chance or other unrelated factors.
• Smoking and Life Expectancy: The null hypothesis asserts that the average life expectancy of smokers is the same as that of non-smokers. Any perceived difference in life expectancy is due to random variation or other factors.
• Brand Preference: The null hypothesis suggests that the proportion of consumers preferring Brand A is the same as those preferring Brand B. Any observed preference in the sample is due to random selection.
• Vaccination Efficacy: The null hypothesis states that the efficacy of Vaccine A does not differ from that of Vaccine B. Any differences observed in a sample are due to chance or other confounding factors.
• Diet and Weight Loss: The null hypothesis proposes that following a specific diet does not result in more weight loss than not following the diet. Any weight loss observed among dieters is considered random or influenced by other factors.
• Exercise and Heart Rate: The null hypothesis states that regular exercise does not lower resting heart rate compared to no exercise. Any lower heart rates observed in exercisers could be due to chance or other unrelated factors.
• Climate Change: The null hypothesis asserts that the average global temperature this decade is not higher than the previous decade. Any observed temperature increase can be attributed to random variation or unaccounted factors.
• Gender Wage Gap: The null hypothesis posits that men and women earn the same average wage for the same job. Any observed wage disparity is due to chance or non-gender related factors.
• Psychotherapy Effectiveness: The null hypothesis states that patients undergoing psychotherapy do not show more improvement than those not undergoing therapy. Any improvement in the
• Energy Drink Consumption and Sleep: The null hypothesis proposes that consuming energy drinks does not affect the quantity of sleep. Any observed differences in sleep duration among energy drink consumers is due to random variation or other factors.
• Organic Food and Health: The null hypothesis asserts that consuming organic food does not lead to better health outcomes compared to consuming non-organic food. Any health differences observed in consumers of organic food are considered random or attributed to other confounding factors.
• Online Learning Effectiveness: The null hypothesis states that students learning online do not perform differently on exams than students learning in traditional classrooms. Any difference in performance can be attributed to chance or unrelated factors.

Null Hypothesis vs Alternative Hypothesis

An alternative hypothesis is the direct contrast to the null hypothesis. It posits that there is a statistically significant relationship or effect between the variables being observed.

If the null hypothesis is rejected based on the test data, the alternative hypothesis is accepted.

Importantly, while the null hypothesis is typically a statement of ‘no effect’ or ‘no difference,’ the alternative hypothesis states that there is an effect or difference.

Comprehension Checkpoint: How does the null hypothesis help to ensure that research is objective and unbiased?

Applications of the Null Hypothesis in Research

The null hypothesis plays a critical role in numerous research settings, promoting objectivity and ensuring findings aren’t due to random chance.

• Clinical Trials: Null hypothesis is used extensively in medical and pharmaceutical research. For example, when testing a new drug’s effectiveness, the null hypothesis might state that the drug has no effect on the disease. If data contradicts this, the null hypothesis is rejected, suggesting the drug might be effective.
• Business and Economics: Businesses use null hypotheses to make informed decisions. For instance, a company might use a null hypothesis to test if a new marketing strategy improves sales. If data suggests a significant increase in sales, the null hypothesis is rejected, and the new strategy may be implemented.
• Psychological Research: Psychologists use null hypotheses to test theories about behavior. For instance, a null hypothesis might state there’s no link between stress and sleep quality. Rejecting this hypothesis based on collected data could help establish a correlation between the two variables.
• Environmental Science: Null hypotheses are used to understand environmental changes. For instance, researchers might form a null hypothesis stating there is no significant difference in air quality before and after a policy change. If this hypothesis is rejected, it indicates the policy may have impacted air quality.
• Education: Educators and researchers often use null hypotheses to improve teaching methods. For example, a null hypothesis might propose a new teaching technique doesn’t enhance student performance. If data contradicts this, the technique may be beneficial.

In all these areas, the null hypothesis helps minimize bias, enabling researchers to support their findings with statistically significant data. It forms the backbone of many scientific research methodologies , promoting a disciplined approach to uncovering new knowledge.

See More Hypothesis Examples Here

The null hypothesis is a cornerstone of statistical analysis and empirical research. It serves as a starting point for investigations, providing a baseline premise that the observed effects are due to chance. By understanding and applying the concept of the null hypothesis, researchers can test the validity of their assumptions, making their findings more robust and reliable. In essence, the null hypothesis ensures that the scientific exploration remains objective, systematic, and free from unintended bias.

• Chris Drew (PhD) https://helpfulprofessor.com/author/chris-drew-phd/ 101 Hidden Talents Examples
• Chris Drew (PhD) https://helpfulprofessor.com/author/chris-drew-phd/ 15 Green Flags in a Relationship
• Chris Drew (PhD) https://helpfulprofessor.com/author/chris-drew-phd/ 15 Signs you're Burnt Out, Not Lazy
• Chris Drew (PhD) https://helpfulprofessor.com/author/chris-drew-phd/ 15 Toxic Things Parents Say to their Children

Leave a Comment Cancel Reply

Your email address will not be published. Required fields are marked *

Null Hypothesis

Ai generator.

Making a certain class or laboratory experiment would require a good null hypothesis . You will be given variables to be used in your experiment and then you would be able to identify the relationship between the two. Every beginning of the experiment report would indicate your hypotheses. It is proven useful for it can be tested to prove if the result is considered false.

What is a Null Hypothesis?

A null hypothesis is used during experiments to prove that there is no difference in the relationship between the two variables. Every type of experiment would require you to make a null hypothesis. From the word itself “null” means zero or no value. If you want to practice making a good experiment report , consider providing a good null hypothesis. Null hypothesis is designed to be rejected if the alternative hypothesis is proven to be exact.

Null Hypothesis Examples in Research

1. medical research.

• Research Question: Does a new drug lower cholesterol levels more effectively than the current drug?
• Null Hypothesis (H0): The new drug has no effect on cholesterol levels compared to the current drug.
• Symbolic Form: H0: ?1 = ?2

2. Educational Research

• Research Question: Does the use of interactive technology improve student test scores?
• Null Hypothesis (H0): Interactive technology does not improve student test scores.

3. Business Research

• Research Question: Does a new marketing strategy increase sales?
• Null Hypothesis (H0): The new marketing strategy does not increase sales.

4. Psychological Research

• Research Question: Does cognitive-behavioral therapy reduce symptoms of anxiety more than standard therapy?
• Null Hypothesis (H0): Cognitive-behavioral therapy does not reduce anxiety symptoms more than standard therapy.

5. Environmental Research

• Research Question: Does urbanization affect bird population diversity?
• Null Hypothesis (H0): Urbanization has no effect on bird population diversity.
• Symbolic Form: H0: ?urban = ?rural

6. Nutritional Research

• Research Question: Does a low-carb diet lead to more weight loss than a low-fat diet?
• Null Hypothesis (H0): A low-carb diet does not lead to more weight loss than a low-fat diet.

7. Economic Research

• Research Question: Does increasing the minimum wage reduce poverty levels?
• Null Hypothesis (H0): Increasing the minimum wage does not reduce poverty levels.
• Symbolic Form: H0: ?before = ?after

8. Sociological Research

• Research Question: Does social media usage affect teenagers’ self-esteem?
• Null Hypothesis (H0): Social media usage does not affect teenagers’ self-esteem.
• Symbolic Form: H0: ?users = ?non-users

9. Agricultural Research

• Research Question: Does the use of a new fertilizer increase crop yield?
• Null Hypothesis (H0): The new fertilizer does not increase crop yield.

10. Technological Research

• Research Question: Does a new software algorithm improve processing speed?
• Null Hypothesis (H0): The new software algorithm does not improve processing speed.
• Symbolic Form: H0: ?new = ?old

Null Hypothesis Examples in Psychology

1. effectiveness of therapy.

• Research Question: Does cognitive-behavioral therapy (CBT) reduce symptoms of depression more effectively than no treatment?
• Null Hypothesis (H0): Cognitive-behavioral therapy does not reduce symptoms of depression more effectively than no treatment.
• Symbolic Form: H0: ?CBT = ?control

2. Impact of Sleep on Memory

• Research Question: Does sleep deprivation affect short-term memory performance?
• Null Hypothesis (H0): Sleep deprivation has no effect on short-term memory performance.
• Symbolic Form: H0: ?sleep_deprived = ?non_sleep_deprived

3. Influence of Color on Mood

• Research Question: Does the color of a room affect individuals’ mood?
• Null Hypothesis (H0): The color of a room does not affect individuals’ mood.
• Symbolic Form: H0: ?color1 = ?color2 = ?color3

4. Social Media and Self-Esteem

• Research Question: Does the frequency of social media use affect teenagers’ self-esteem?
• Null Hypothesis (H0): The frequency of social media use does not affect teenagers’ self-esteem.
• Symbolic Form: H0: ?high_use = ?low_use

5. Mindfulness and Stress Reduction

• Research Question: Does mindfulness meditation reduce stress levels in college students?
• Null Hypothesis (H0): Mindfulness meditation does not reduce stress levels in college students.
• Symbolic Form: H0: ?mindfulness = ?control

6. Parenting Styles and Academic Performance

• Research Question: Does authoritative parenting style affect children’s academic performance?
• Null Hypothesis (H0): Authoritative parenting style does not affect children’s academic performance.
• Symbolic Form: H0: ?authoritative = ?other_styles

7. Impact of Exercise on Anxiety

• Research Question: Does regular exercise reduce anxiety levels in adults?
• Null Hypothesis (H0): Regular exercise does not reduce anxiety levels in adults.
• Symbolic Form: H0: ?exercise = ?no_exercise

8. Gender Differences in Risk-Taking Behavior

• Research Question: Are there differences in risk-taking behavior between males and females?
• Null Hypothesis (H0): There are no differences in risk-taking behavior between males and females.
• Symbolic Form: H0: ?males = ?females

9. Impact of Music on Concentration

• Research Question: Does listening to music while studying affect concentration levels?
• Null Hypothesis (H0): Listening to music while studying does not affect concentration levels.
• Symbolic Form: H0: ?music = ?no_music

10. Effect of Group Therapy on Social Skills

• Research Question: Does group therapy improve social skills in individuals with social anxiety?
• Null Hypothesis (H0): Group therapy does not improve social skills in individuals with social anxiety.
• Symbolic Form: H0: ?group_therapy = ?no_therapy

Null Hypothesis Examples in Biology

1. effect of fertilizers on plant growth.

• Research Question: Does a new fertilizer improve plant growth compared to no fertilizer?
• Null Hypothesis (H0): The new fertilizer does not improve plant growth compared to no fertilizer.
• Symbolic Form: H0: ?fertilizer = ?no_fertilizer

2. Antibiotic Effectiveness on Bacteria

• Research Question: Does a new antibiotic reduce bacterial growth more effectively than an existing antibiotic?
• Null Hypothesis (H0): The new antibiotic does not reduce bacterial growth more effectively than the existing antibiotic.
• Symbolic Form: H0: ?new_antibiotic = ?existing_antibiotic

3. Impact of Temperature on Enzyme Activity

• Research Question: Does temperature affect the activity of a specific enzyme?
• Null Hypothesis (H0): Temperature does not affect the activity of the specific enzyme.
• Symbolic Form: H0: Enzyme activity at temperature1 = Enzyme activity at temperature2

4. Genetic Influence on Trait Expression

• Research Question: Does a specific gene affect the expression of a particular trait in a plant species?
• Null Hypothesis (H0): The specific gene does not affect the expression of the particular trait in the plant species.
• Symbolic Form: H0: Trait expression with gene = Trait expression without gene

5. Effect of Light Intensity on Photosynthesis

• Research Question: Does light intensity affect the rate of photosynthesis in plants?
• Null Hypothesis (H0): Light intensity does not affect the rate of photosynthesis in plants.
• Symbolic Form: H0: Photosynthesis rate at light intensity1 = Photosynthesis rate at light intensity2

6. Impact of Diet on Animal Growth

• Research Question: Does a high-protein diet affect the growth rate of animals?
• Null Hypothesis (H0): A high-protein diet does not affect the growth rate of animals.
• Symbolic Form: H0: Growth rate on high-protein diet = Growth rate on normal diet

7. Effect of Pollution on Aquatic Life

• Research Question: Does water pollution affect the survival rate of fish in a lake?
• Null Hypothesis (H0): Water pollution does not affect the survival rate of fish in a lake.
• Symbolic Form: H0: Fish survival in polluted water = Fish survival in non-polluted water

8. Impact of Caffeine on Heart Rate in Daphnia

• Research Question: Does caffeine affect the heart rate of Daphnia (water fleas)?
• Null Hypothesis (H0): Caffeine does not affect the heart rate of Daphnia.
• Symbolic Form: H0: Heart rate with caffeine = Heart rate without caffeine

9. Influence of Soil pH on Plant Germination

• Research Question: Does soil pH affect the germination rate of seeds?
• Null Hypothesis (H0): Soil pH does not affect the germination rate of seeds.
• Symbolic Form: H0: Germination rate at pH1 = Germination rate at pH2

10. Effect of Salinity on Aquatic Plant Growth

• Research Question: Does salinity affect the growth of aquatic plants?
• Null Hypothesis (H0): Salinity does not affect the growth of aquatic plants.
• Symbolic Form: H0: Plant growth in saline water = Plant growth in freshwater

Null Hypothesis Examples in Business

1. effect of marketing campaign on sales.

• Research Question: Does a new marketing campaign increase product sales?
• Null Hypothesis (H0): The new marketing campaign does not increase product sales.
• Symbolic Form: H0: ?campaign = ?no_campaign

2. Impact of Training Programs on Employee Productivity

• Research Question: Do training programs improve employee productivity?
• Null Hypothesis (H0): Training programs do not improve employee productivity.
• Symbolic Form: H0: ?trained = ?untrained

3. Influence of Price Changes on Demand

• Research Question: Do price changes affect the demand for a product?
• Null Hypothesis (H0): Price changes do not affect the demand for the product.
• Symbolic Form: H0: ?price_change = ?no_price_change

4. Customer Satisfaction and Service Quality

• Research Question: Does improving service quality increase customer satisfaction?
• Null Hypothesis (H0): Improving service quality does not increase customer satisfaction.
• Symbolic Form: H0: ?improved_service = ?standard_service

5. Effect of Employee Benefits on Retention Rates

• Research Question: Do enhanced employee benefits reduce turnover rates?
• Null Hypothesis (H0): Enhanced employee benefits do not reduce turnover rates.
• Symbolic Form: H0: ?enhanced_benefits = ?standard_benefits

6. Impact of Social Media Presence on Brand Awareness

• Research Question: Does an active social media presence increase brand awareness?
• Null Hypothesis (H0): An active social media presence does not increase brand awareness.
• Symbolic Form: H0: ?active_social_media = ?inactive_social_media

7. Influence of Store Layout on Customer Purchases

• Research Question: Does store layout affect customer purchasing behavior?
• Null Hypothesis (H0): Store layout does not affect customer purchasing behavior.
• Symbolic Form: H0: ?layout1 = ?layout2

8. Online Advertising and Website Traffic

• Research Question: Does online advertising increase website traffic?
• Null Hypothesis (H0): Online advertising does not increase website traffic.
• Symbolic Form: H0: ?ads = ?no_ads

9. Effect of Product Packaging on Sales

• Research Question: Does new product packaging design increase sales?
• Null Hypothesis (H0): The new product packaging design does not increase sales.
• Symbolic Form: H0: ?new_packaging = ?old_packaging

10. Influence of Remote Work on Employee Performance

• Research Question: Does remote work affect employee performance?
• Null Hypothesis (H0): Remote work does not affect employee performance.
• Symbolic Form: H0: ?remote_work = ?office_work

Null Hypothesis Examples in Statistics

1. comparing means.

• Research Question: Is there a difference in average test scores between two groups of students?
• Null Hypothesis (H0): There is no difference in the average test scores between the two groups.

2. Proportions

• Research Question: Is the proportion of defective products the same in two different production lines?
• Null Hypothesis (H0): The proportion of defective products is the same in both production lines.
• Symbolic Form: H0: p1 = p2

3. Regression Analysis

• Research Question: Is there a relationship between years of experience and salary?
• Null Hypothesis (H0): There is no relationship between years of experience and salary.
• Symbolic Form: H0: ? = 0 (where ? is the regression coefficient)

4. ANOVA (Analysis of Variance)

• Research Question: Are the means of three or more groups equal?
• Null Hypothesis (H0): The means of all groups are equal.
• Symbolic Form: H0: ?1 = ?2 = ?3 = … = ?k

5. Chi-Square Test for Independence

• Research Question: Are gender and voting preference independent?
• Null Hypothesis (H0): Gender and voting preference are independent.
• Symbolic Form: H0: There is no association between gender and voting preference.

6. Time Series Analysis

• Research Question: Does a time series exhibit a trend over time?
• Null Hypothesis (H0): There is no trend in the time series data over time.
• Symbolic Form: H0: The time series has no significant trend component.

7. Hypothesis Testing for Variance

• Research Question: Is the variance in test scores different between two classes?
• Null Hypothesis (H0): The variances in test scores are equal between the two classes.
• Symbolic Form: H0: ?1² = ?2²

8. Correlation Analysis

• Research Question: Is there a correlation between two variables, such as height and weight?
• Null Hypothesis (H0): There is no correlation between the two variables.
• Symbolic Form: H0: ? = 0 (where ? is the correlation coefficient)

9. Two-Sample t-Test

• Research Question: Do two samples have the same mean?
• Null Hypothesis (H0): The two samples have the same mean.

10. One-Sample t-Test

• Research Question: Does the sample mean differ from a known population mean?
• Null Hypothesis (H0): The sample mean is equal to the population mean.
• Symbolic Form: H0: ? = ?0

Real life Examples of Null Hypothesis

1. medical studies.

• Research Question: Does a new medication lower blood pressure more effectively than the current medication?
• Null Hypothesis (H0): The new medication does not lower blood pressure more effectively than the current medication.
• Example: A clinical trial compares blood pressure readings between patients taking the new medication and those taking the current medication.

2. Education

• Research Question: Does a new teaching method improve student test scores?
• Null Hypothesis (H0): The new teaching method does not improve student test scores.
• Example: An educational study compares test scores of students taught using the new method versus those taught using traditional methods.

3. Business

• Research Question: Does a new advertising campaign increase product sales?
• Null Hypothesis (H0): The new advertising campaign does not increase product sales.
• Example: A company runs the new campaign and compares sales data before and after the campaign.

4. Public Health

• Research Question: Does a smoking cessation program reduce the smoking rate in a community?
• Null Hypothesis (H0): The smoking cessation program does not reduce the smoking rate in the community.
• Example: Public health officials analyze smoking rates before and after implementing the program.

5. Environmental Science

• Research Question: Does the introduction of a specific fish species affect the biodiversity of a lake?
• Null Hypothesis (H0): The introduction of the specific fish species does not affect the biodiversity of the lake.
• Example: Environmental scientists monitor biodiversity levels before and after introducing the fish species.

6. Economics

• Research Question: Does raising the minimum wage reduce poverty levels?
• Null Hypothesis (H0): Raising the minimum wage does not reduce poverty levels.
• Example: Economists compare poverty rates in regions with and without recent minimum wage increases.

7. Psychology

• Research Question: Does mindfulness meditation reduce stress levels among college students?
• Null Hypothesis (H0): Mindfulness meditation does not reduce stress levels among college students.
• Example: A study measures stress levels before and after a mindfulness meditation program in a group of students.

8. Agriculture

• Example: Farmers apply the new fertilizer to one field and a standard fertilizer to another and compare the yields.

9. Technology

• Research Question: Does a new software update improve the speed of a computer program?
• Null Hypothesis (H0): The new software update does not improve the speed of the computer program.
• Example: Software engineers measure the program’s speed before and after applying the update.

10. Marketing

• Research Question: Does personalized email marketing increase customer engagement?
• Null Hypothesis (H0): Personalized email marketing does not increase customer engagement.
• Example: A company sends personalized emails to one group and generic emails to another, then compares engagement rates.

More Null Hypothesis Examples & Samples in PDF

1. null hypothesis significance test example.

2. Sample Null Hypothesis Example

3. Critical Assessment of Null Hypothesis Example

4. Confidence Levels for Null Hypotheses Example

5. Interpreting Failure to Reject A Null Hypothesis Example

6. Simple Null Hypothesis Example

7. Basic Neurology Null Hypothesis Example

8. Null Research Hypothesis in DOC

Purpose of Null Hypothesis

The null hypothesis is a fundamental concept in statistics and scientific research . It serves several critical purposes in the process of hypothesis testing, guiding researchers in drawing meaningful conclusions from their data. Below are the primary purposes of the null hypothesis:

1. Baseline for Comparison

The null hypothesis provides a baseline or a default position that indicates no effect, no difference, or no relationship between variables. It is the statement that researchers aim to test against an alternative hypothesis. By starting with the assumption that there is no effect, researchers can objectively assess whether the data provide enough evidence to support the alternative hypothesis.

2. Eliminates Bias

By assuming no effect or no difference, the null hypothesis helps eliminate bias in research. Researchers approach their study without preconceived notions about the outcome, ensuring that the results are based on the data collected rather than personal beliefs or expectations.

3. Framework for Statistical Testing

The null hypothesis provides a structured framework for conducting statistical tests. It is essential for calculating p-values and test statistics, which determine whether the observed data are significantly different from what would be expected under the null hypothesis. This framework allows for a standardized approach to testing hypotheses across various fields of study.

4. Facilitates Decision Making

The null hypothesis facilitates decision-making in research by providing clear criteria for accepting or rejecting it. If the data provide sufficient evidence to reject the null hypothesis, researchers can conclude that there is a statistically significant effect or difference. This decision-making process is critical in advancing scientific knowledge and understanding.

5. Controls Type I and Type II Errors

The null hypothesis plays a crucial role in controlling Type I and Type II errors in hypothesis testing. A Type I error occurs when the null hypothesis is incorrectly rejected (a false positive), while a Type II error happens when the null hypothesis is incorrectly accepted (a false negative). By defining the null hypothesis, researchers can set significance levels (e.g., alpha level) to manage the risk of these errors.

When is the Null Hypothesis Rejected?

Rejecting the null hypothesis is a critical step in the process of hypothesis testing. The decision to reject the null hypothesis is based on statistical evidence derived from the data collected in a study. Below are the key factors that determine when the null hypothesis is rejected:

The p-value is a measure of the probability that the observed data (or something more extreme) would occur if the null hypothesis were true. The null hypothesis is rejected if the p-value is less than or equal to the predetermined significance level (?).

• Significance Level (?): This is the threshold set by the researcher, commonly 0.05 (5%). If the p-value ? 0.05, the null hypothesis is rejected.
• If a p-value of 0.03 is obtained and the significance level is 0.05, the null hypothesis is rejected.

2. Test Statistic

The test statistic is a standardized value calculated from sample data during a hypothesis test. It measures the degree to which the sample data differ from the null hypothesis. The decision to reject the null hypothesis depends on whether the test statistic falls within the critical region.

• Critical Region: This is determined by the significance level and the distribution of the test statistic (e.g., Z-distribution, t-distribution).
• In a two-tailed test with ? = 0.05, the critical region for a Z-test might be Z < -1.96 or Z > 1.96. If the test statistic is 2.10, the null hypothesis is rejected.

3. Confidence Intervals

Confidence intervals provide a range of values that are likely to contain the population parameter. If the confidence interval does not include the value specified by the null hypothesis, the null hypothesis is rejected.

• If a 95% confidence interval for the mean difference between two groups is (2.5, 5.0) and the null hypothesis states that the mean difference is 0, the null hypothesis is rejected.

4. Effect Size

Effect size measures the magnitude of the difference between groups or the strength of a relationship between variables. While not a direct criterion for rejecting the null hypothesis, a substantial effect size can support the decision to reject the null hypothesis when combined with a significant p-value.

Null Hypothesis vs. Alternative Hypothesis

How to Write a Null Hypothesis

Writing a null hypothesis is a crucial step in designing a scientific study or experiment. The null hypothesis (H0) serves as a starting point for statistical testing and represents a statement of no effect or no difference. Here’s a step-by-step guide on how to write a null hypothesis:

1. Identify the Research Question

Start by clearly defining the research question you want to investigate. Understand what you are testing and what you expect to find.

• Example Research Question: Does a new medication reduce blood pressure more effectively than an existing medication?

2. Determine the Variables

Identify the independent and dependent variables in your study.

• Independent Variable: The variable that is manipulated or categorized (e.g., type of medication).
• Dependent Variable: The variable that is measured or observed (e.g., blood pressure).

3. State the Null Hypothesis Clearly

The null hypothesis should assert that there is no effect, no difference, or no relationship between the variables. It is usually written as a statement of equality or no change.

• Format: “There is no [effect/difference/relationship] in [dependent variable] between [independent variable groups].”
• Example: “There is no difference in blood pressure reduction between the new medication and the existing medication.”

4. Use Proper Symbols and Notation

In formal scientific writing, use symbols and proper notation to represent the null hypothesis.

• Here, ?1 represents the mean blood pressure reduction for the new medication, and ?2 represents the mean blood pressure reduction for the existing medication.

Why is the null hypothesis important?

The null hypothesis is crucial as it provides a baseline for comparison and allows researchers to test the significance of their findings.

How do you state a null hypothesis?

A null hypothesis is stated as no effect or no difference, typically in the form “There is no [effect/difference] between [groups/variables].”

What is the alternative hypothesis?

The alternative hypothesis (H1) suggests that there is an effect or difference between variables, opposing the null hypothesis.

What does it mean to reject the null hypothesis?

Rejecting the null hypothesis means the data provides sufficient evidence to support the alternative hypothesis, indicating a significant effect or difference.

What is a p-value?

A p-value measures the probability that the observed data would occur if the null hypothesis were true. Low p-values indicate strong evidence against the null hypothesis.

What is a Type I error?

A Type I error occurs when the null hypothesis is incorrectly rejected, meaning a false positive result is concluded.

What is a Type II error?

A Type II error happens when the null hypothesis is incorrectly accepted, meaning a false negative result is concluded.

How do you choose a significance level (?)?

The significance level, often set at 0.05, is chosen based on the acceptable risk of making a Type I error in the context of the study.

Can the null hypothesis be proven true?

No, the null hypothesis can only be rejected or not rejected. Failing to reject it does not prove it true, only that there is not enough evidence against it.

What is the role of sample size in hypothesis testing?

Larger sample sizes increase the test’s power, reducing the risk of Type II errors and making it easier to detect a true effect.

Text prompt

• Instructive
• Professional

10 Examples of Public speaking

20 Examples of Gas lighting

• Math Article

Null Hypothesis

In mathematics, Statistics deals with the study of research and surveys on the numerical data. For taking surveys, we have to define the hypothesis. Generally, there are two types of hypothesis. One is a null hypothesis, and another is an alternative hypothesis .

In probability and statistics, the null hypothesis is a comprehensive statement or default status that there is zero happening or nothing happening. For example, there is no connection among groups or no association between two measured events. It is generally assumed here that the hypothesis is true until any other proof has been brought into the light to deny the hypothesis. Let us learn more here with definition, symbol, principle, types and example, in this article.

Table of contents:

• Comparison with Alternative Hypothesis

Null Hypothesis Definition

The null hypothesis is a kind of hypothesis which explains the population parameter whose purpose is to test the validity of the given experimental data. This hypothesis is either rejected or not rejected based on the viability of the given population or sample . In other words, the null hypothesis is a hypothesis in which the sample observations results from the chance. It is said to be a statement in which the surveyors wants to examine the data. It is denoted by H 0 .

Null Hypothesis Symbol

In statistics, the null hypothesis is usually denoted by letter H with subscript ‘0’ (zero), such that H 0 . It is pronounced as H-null or H-zero or H-nought. At the same time, the alternative hypothesis expresses the observations determined by the non-random cause. It is represented by H 1 or H a .

Null Hypothesis Principle

The principle followed for null hypothesis testing is, collecting the data and determining the chances of a given set of data during the study on some random sample, assuming that the null hypothesis is true. In case if the given data does not face the expected null hypothesis, then the outcome will be quite weaker, and they conclude by saying that the given set of data does not provide strong evidence against the null hypothesis because of insufficient evidence. Finally, the researchers tend to reject that.

Null Hypothesis Formula

Here, the hypothesis test formulas are given below for reference.

The formula for the null hypothesis is:

H 0 :  p = p 0

The formula for the alternative hypothesis is:

H a = p >p 0 , < p 0 ≠ p 0

The formula for the test static is:

Remember that,  p 0  is the null hypothesis and p – hat is the sample proportion.

Also, read:

Types of Null Hypothesis

There are different types of hypothesis. They are:

Simple Hypothesis

It completely specifies the population distribution. In this method, the sampling distribution is the function of the sample size.

Composite Hypothesis

The composite hypothesis is one that does not completely specify the population distribution.

Exact Hypothesis

Exact hypothesis defines the exact value of the parameter. For example μ= 50

Inexact Hypothesis

This type of hypothesis does not define the exact value of the parameter. But it denotes a specific range or interval. For example 45< μ <60

Null Hypothesis Rejection

Sometimes the null hypothesis is rejected too. If this hypothesis is rejected means, that research could be invalid. Many researchers will neglect this hypothesis as it is merely opposite to the alternate hypothesis. It is a better practice to create a hypothesis and test it. The goal of researchers is not to reject the hypothesis. But it is evident that a perfect statistical model is always associated with the failure to reject the null hypothesis.

How do you Find the Null Hypothesis?

The null hypothesis says there is no correlation between the measured event (the dependent variable) and the independent variable. We don’t have to believe that the null hypothesis is true to test it. On the contrast, you will possibly assume that there is a connection between a set of variables ( dependent and independent).

When is Null Hypothesis Rejected?

The null hypothesis is rejected using the P-value approach. If the P-value is less than or equal to the α, there should be a rejection of the null hypothesis in favour of the alternate hypothesis. In case, if P-value is greater than α, the null hypothesis is not rejected.

Null Hypothesis and Alternative Hypothesis

Now, let us discuss the difference between the null hypothesis and the alternative hypothesis.

Null Hypothesis Examples

Here, some of the examples of the null hypothesis are given below. Go through the below ones to understand the concept of the null hypothesis in a better way.

If a medicine reduces the risk of cardiac stroke, then the null hypothesis should be “the medicine does not reduce the chance of cardiac stroke”. This testing can be performed by the administration of a drug to a certain group of people in a controlled way. If the survey shows that there is a significant change in the people, then the hypothesis is rejected.

Few more examples are:

1). Are there is 100% chance of getting affected by dengue?

Ans: There could be chances of getting affected by dengue but not 100%.

2). Do teenagers are using mobile phones more than grown-ups to access the internet?

Ans: Age has no limit on using mobile phones to access the internet.

3). Does having apple daily will not cause fever?

Ans: Having apple daily does not assure of not having fever, but increases the immunity to fight against such diseases.

4). Do the children more good in doing mathematical calculations than grown-ups?

Ans: Age has no effect on Mathematical skills.

In many common applications, the choice of the null hypothesis is not automated, but the testing and calculations may be automated. Also, the choice of the null hypothesis is completely based on previous experiences and inconsistent advice. The choice can be more complicated and based on the variety of applications and the diversity of the objectives. 

The main limitation for the choice of the null hypothesis is that the hypothesis suggested by the data is based on the reasoning which proves nothing. It means that if some hypothesis provides a summary of the data set, then there would be no value in the testing of the hypothesis on the particular set of data. 

Frequently Asked Questions on Null Hypothesis

What is meant by the null hypothesis.

In Statistics, a null hypothesis is a type of hypothesis which explains the population parameter whose purpose is to test the validity of the given experimental data.

What are the benefits of hypothesis testing?

Hypothesis testing is defined as a form of inferential statistics, which allows making conclusions from the entire population based on the sample representative.

When a null hypothesis is accepted and rejected?

The null hypothesis is either accepted or rejected in terms of the given data. If P-value is less than α, then the null hypothesis is rejected in favor of the alternative hypothesis, and if the P-value is greater than α, then the null hypothesis is accepted in favor of the alternative hypothesis.

Why is the null hypothesis important?

The importance of the null hypothesis is that it provides an approximate description of the phenomena of the given data. It allows the investigators to directly test the relational statement in a research study.

How to accept or reject the null hypothesis in the chi-square test?

If the result of the chi-square test is bigger than the critical value in the table, then the data does not fit the model, which represents the rejection of the null hypothesis.

Put your understanding of this concept to test by answering a few MCQs. Click ‘Start Quiz’ to begin!

Select the correct answer and click on the “Finish” button Check your score and answers at the end of the quiz

Visit BYJU’S for all Maths related queries and study materials

Your result is as below

Request OTP on Voice Call

Register with BYJU'S & Download Free PDFs

Register with byju's & watch live videos.